Question 642107
 bob takes escalator from subway to street level. 
 if he runs-up 8 stairs it takes him 46.5 seconds.
 if he runs-up 13 stairs it takes him 39.0 seconds.
How long will it take bob to get to the top if he doesn't run at all?
:
let s = no. of steps traveled by the escalator
then
(s+8) = no. of steps when he runs up in 46.5 sec
and
(s+13) = no. of steps when he runs up in 39 sec
:
Let d = total distance traveled by the escalator
then
{{{d/((s+8)))}}} = 46.5
d = 46.5(s+8)
and
{{{d/((s+13))}}} = 39
d = 39(s+13)
:
d=d, therefore we can combine the equations
46.5(s+8) = 39(s+13)
46.5s + 372 = 39s + 507
46.5s - 39s = 507 - 372
7.5s = 135
s = 135/7.5
s = 18 steps
:
Find the time (t) when just letting escalator move
Time varies inversely with speed
{{{t/39}}} = {{{(18+13)/18}}}
{{{t/39}}} = {{{31/18}}}
cross multiply
18t = 39 * 31
18t = 1209
t = 1209/18
t = 67.2 seconds if he just ride it